Wilcoxon signed-rank test
The Wilcoxon signed-rank test is a non-parametric alternative to the paired t-test: it ranks absolute paired differences and compares the summed positive and negative ranks to test whether the median difference is zero.
What it is
See it move
The Wilcoxon signed-rank test ranks the absolute paired differences, reattaches their sign, then compares the two rank sums. Six branches' before/after sales differences of +1, −2, +3, −4, +5, +6 rank 1 through 6 with no ties. Positive differences carry ranks 1, 3, 5 and 6, summing to 15; negative differences carry ranks 2 and 4, summing to 6. The test statistic W is the smaller sum, W = 6.
The formula
Variables
- Wilcoxon signed-rank test statistic
- Sum of ranks assigned to positive paired differences
- Sum of ranks assigned to negative paired differences
Gives the Wilcoxon signed-rank test statistic from the two rank sums; a small W relative to its critical value signals the paired differences are not centred on zero.
Check yourself
Five paired before/after scores are converted into ranked absolute differences, and each rank is given back its original sign: +1, +2, +3, −4, +5. What is the Wilcoxon signed-rank test statistic W, the smaller of the positive and negative rank sums?